Pure Definition and 482 Threads

Hello PF! I was reading https://en.wikipedia.org/wiki/Fubini–Study_metric (qm section like always :wink:) And can't figure out how to derive: \gamma (\psi , \phi) = arccos \sqrt{\frac{<\psi|\phi><\phi|\psi>}{<\psi|\psi><\phi|\phi>}} I started with \gamma (\psi , \phi) =|| |\psi> - |\phi>||=...

Hi, So I am currently a mechanical engineer working in aerospace designing and testing different interior assemblies, video arms, meal tables, etc. For a while now I have been thinking that this field is just not up my alley. I probably use Creo for about 80% of my time while the other 20% I am...

Hello. The textbook that was assigned to my class is not a good fit for my professor. The textbook simplifies the basic force equations so that there are no general equations with integrals or vector calculus calculations. Can anybody recommend a Fluid Mechanics book or books that deal only...

Hi. 1. Does a pure state belong to mixed states \hat{\rho}=\sum_k p_k|\psi_k><\psi_k| where ##p_k=1## for k=i and otherwise 0 ? 2. Does quantum jump by observation work for both mixed and pure states ? Your teachings will be appreciated.

Hello guys, I am trying to understand the following experiment: 1. Prepare a 2 level atom in state |0> 2. Shine in a Pi/2 pulse --> atom goes to 1/√2 (|0>+|1>) 3. Wait time T 4. Shine in second Pi/2 pulse a) if the state is pure: atom will go to state |1>, p1=1 b) if the state is...

According to decoherance. Say there is a pure state initially in state: |ψ⟩=α|0⟩+β|1⟩ After decoherance (interaction with environment), the system will transform into the improper mixed state of: ρ=|α|2|0⟩⟨0|+|β|2|1⟩⟨1| This is the "apparent" collapse that decoherance refers to. With the...

Hey guys, I am having issues with understanding the physical nature of pure and mixed states. Maybe you can help me out? 1) A pure state - superposition is a state that consists of different states at the same time. It's like having several waves, each one belonging to an Eigenstate of the...

How much pure disinfectant must be added to 30 gallons of an 8% solution to increase its strength by 25%? Let x = pure disinfectant to be added The word PURE tells me that 100 will be in the equation somewhere. 30 gallons of 8 percent = 0.08(30) Must be added to some unknown = plus x My...

A chemist needs a 30% acid solution. How much pure acid needs to be mixed with 5 milliliter a of a 10% acid solution to obtain the desired solution? The words PURE ACID for some reason or another point to 100 percent. My equation: 0.30(x) + 0.10(5) = (x + 5) Is this right?

Then it goes on explaining how Gauss law would fail because for a very large surface, E field would be vanish with flux through it and though we can calculate div for this field it won't depend on source density. But I don't get what makes this particular function so evil that it would break...

I'm currently finishing up my second year in college and I'm expected to graduate on time (in two years) and I'm majoring in pure physics. I don't really fully understand the difference between applied physics and pure physics because anytime I look into it online there's 10 different answers...

The book says when the water is heated, the pressure stays constant. But I do not understand pressure for a liquid-water system. What is the pressure for a liquid here? the pressure on the surface, botton or sides? Source: Fundamentals of Thermodynamics by Sonntag/Borgnakke/Van Wylen. Thank you.

Hi everyone! If I have a sample that didn’t present conductivity and left a solid evaporation residue but its density is approximately 1 g/mL (1,08 g/mL), can I still say it is pure water? I suppose pure water shouldn’t have any kind of solid residue. Thanks!

Homework Statement Two solid spheres one of mass 'm' and other of mass '2m' are comin towards each other(translationally) with a velocity v1 and v2.After collision the sphere of mass 2m comes to rest and the sphere of mass m does oblique projectile motion at an angle 30 with the vertical till...

I just found that applying an axial load of magnitude σ on both sides of a ductile rod will produce a max in plane shear stress of magnitude σ/2. Why is this? How can there be shear stress if only a normal force is applied?

what does it mean that a particle is a pure eigenstate? could someone explain this to me simply ?

Hello everyone, Today I'm asking you for help to put together these two equations of state for high densities BPS-BBP with a eos of a pure neutron gas or a non interacting n + p + e gas. I have already the data of BPS-BBP equation of state, with includes neutron drip and let a open space to...

Can you create pure semiconductor quantum dots? I have seen composite ones that are created with elements in the group II-VI and III-V. Moreover, it saids that the size of the quantum dots must smaller than the Bohr Excitron Radius. From my understanding of the Bohr Exciton Radius is the...

Hi, I am wanting some advice on about studying applied math or pure math. I have finished my 2nd year at uni and will be starting my 3rd year soon and have been thinking about changing my major from pure to applied (I also major in statistics as well). After I graduate I would love to do...

Is it worth doing pure math if you're not going into academia? Would it be a bad idea to get your bachelors in pure math and stop there? Is pure math just something for people who want to go on to grad school? I'm just not sure if there are good job prospects for someone with a bachelors in...

Consider three identical boxes of volume V. the first two boxes will contain particles of two different species 'N' and 'n'. The first box contains 'N' identical non interacting particles in a volume V. The second box contains 'n' non interacting particles. The third box is the result of mixing...

Is there a material that changes from transparent to a pure white, ideally with reflective ability. Smart glass almost does this but falls short on it but being white enough (and not reflective).

Consider pure water separated from an aqueous starch solution by a semipermeable membrane, which allows water to pass freely but not starch. After some time has elapsed, the concentration of starch solution a. will have increased b. will have decreased c. will not have changed d. might have...

Homework Statement Archimedes, prove your stuff. A royal crown (cola?) of pure gold is suspended in air by a thread and the tension in the thread is of magnitude T. When the crown is totally immersed in water, the magnitude of the tension in the thread is 0.872T. A) sketch a second law force...

Homework Statement The only things you know about the sample are: (i) it has some kind of cubic lattice, and (ii) it is a pure element. Identify the element in the crystalline sample. SC: R = 0.5a FCC: R = 0.25a√2 BCC: R = 0.25a√3 Distances from Bragg peaks: d1 = 0.2037 nm d2 = 0.1746 nm d3...

According to atty.. entangled system are pure (can be in superposition) while according to Bill.. entangled system are not pure (not in superposition) Here's the prove of what they stated: atty said...

I learned about pure state, mixed state, reduce density matrix, etc. from this now famous paper http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf (thanks to Bill) I'd like to know something. Atty said somewhere: "A pure state means that we have prepared many copies of...

have a nice day. I was torn between mathematics and physics. I do not know which one I wanted. How can I decide? for me; theoretical physics, applied mathematics - topology (dif.topology, alg.topology, geom.topology), differential geometry easy than pure, proof based mathemics. I'm better...

Consider a simple two level atom system,|1>,|2> (not degenerate) interacted with monochromatic laser, of which the frequency is exactly resonant with the |1> to |2> transition. The evolution start from {1>. As far as I understand, the dressed degenerate state |1>|n> and |2>|n-1> will get...

Homework Statement to resist the bending, there must be reaction force(blue) act against the applied force(red), the reaction force that resist bending is the longitidunal normal force , right? why the author stated it as longitidunal shear force, is it wrong? Homework EquationsThe Attempt at...

Homework Statement in the notes , i was told that when pure bending occur, there is no shear force acting... Homework EquationsThe Attempt at a Solution refer to diagram 3.11 , does it mean the center of beam (between 2 forces P) will break? since there's no shear force acting

Currently I am studying a double major in Math and Physics, hopefully leading towards experimental physics, however come next semester I will have to pick my math "specialisations" from two of applied math (mostly chaos and optimisation etc.), pure math(mostly abstract algebra and analysis) and...

Is there any experimental evidence that pure energy (massless) can curve spacetime?

I am off to start a physics degree in September, with the aim of going into theoretical research. However, for this I feel my pure maths skills need to be better. I know in a physics degree I will learn how to use pure maths (how to solve differential equation, how to use matrices, how to use...

If I have a spin 1/2 particle eg electron in an isolated box can I state for definite that there is a 50% chance of it being spin up and 50% spin down ? If I know the probability of it being spin up and spin down how do I know if it exists as a pure state of a superposition of spin up and spin...

I know in Calculus there is a pure vs. applied calc. distinction. I took Applied Calculus last year, but not the pure form. I've been checking out my university's math catalog and they bring up an applied math vs. pure math track. I can see that applied math is math that is used in specific...

looking at notes on functional analysis for self study. the authors I have stumbled across so far launch straight into the formal theory. I can't find any middle ground of intuitive motivations for the theory as yet. I am assuming the following is part of set theory? I can't follow the arguments...

Hi guys, I was wondering if it is possible to have a pure planar rotation of a rectangular-prism shaped rigid body on a planar surface when it is subjected to a planar point force at the tip. Is there any range for the point force such that it can not break the static friction force (so no...

why change of volume in pure torsion is zero? if you consider stress in plane with degree of 45 there is normal stress normal stress can lead to change of volume

When I ask about mass, I am really asking is it remotely possible for pure energy to have mass and possible become so dense it forms a ball with its own gravitational pull. This pull keeps the energy in a ball.

I have a big choice to make which is not letting me sleep or study properly. For the last few years I have been attending community college. For financial reasons I left school during the 9th grade. Both of my parents were terminally ill. My father passed away, my mother still lives. I placed...

I got (very) confused about the concept of states, pure states and mixed states. Is it correct that a linear combination of pure states is another pure state? Can pure (and mixed) states only be expressed in density matrices? Is a pure state expressed in a single density matrix, whereas mixed...

Please don't hate if this is a stupid question, I am a freshmen in high school so I don't know this stuff. What I am really talking about is how all atoms have some impurity in them which is why friction happens, but is there a way to create one with no impurity?

micromass submitted a new PF Insights post How to Self Study Geometry. Part I: Pure Geometry Continue reading the Original PF Insights Post.

I am not an expert in the field, but intuitively I think that a resume with both math and computer science has a lot of impact. I also think that math can help me understand computer science better. Next quarter, I am planning to take classical geometry, so I am just wondering if this class...

Homework Statement Hellooo, so this is the question that i have: A 0.5-m3 rigid tank initially contained a saturated liquid-vapor mixture of water at 140 °C is now heated until the mixture reaches the critical state. Determine the mass and the volume of liquid before the heating process...

Homework Statement In which one of the following solutions is silver chloride the most soluble? A) 0.181 M HCl B) 0.0176 M NH3 C) 0.744 M LiNO3 D) pure water E) 0.181 M NaCl Homework Equations the Ksp expression for the dissolution of AgCl is: Ksp = [Ag+][Cl-]The Attempt at a Solution...

I've asked many... what does it mean to major in math (pure). I am a first year sophomore and still undecided about my major.I used to get full marks on math tests n high school, but how can I know if I'm able to be something in math. Anyone can learn how to do math, but few can actually make...

\Homework Statement Show that the Fidelity between one pure state |\Psi\rangle and one arbitrary state \rho is given by F(|\Psi\rangle , \rho)=\sqrt{\langle\Psi|\rho|\Psi\rangle} . Homework Equations The quantum mechanical fidelity is defined as \begin{equation*}...

I am looking for a book concerning the foundations of mathematics. I am not talking about algebra or calculus but the foundation of the mathematical language( Axioms, sentential logic...). I hope you have understood the prior rubish. Thanks for any help.